在 C++ 中分配大内存块

I am trying to allocate a large memory block for a 3D matrix in C++ of floating point value. It's dimensions are 44100x2200x2. This should take exactly 44100x2200x2x4 bytes of memory which is about 7.7gb. I am compiling my code using g++ on a 64bit x86 machine with Ubuntu. When I view the process using htop, I see that the memory usage grows to 32gb and is promptly killed. Did I make a mistake in my memory calculation?

这是我的代码:

#include <iostream>

using namespace std;
int main(int argc, char* argv[]) {
  int N = 22000;
  int M = 44100;
  float*** a = new float**[N];
  for (int m = 0; m<N; m+=1) {
    cout<<((float)m/(float)N)<<endl;
    a[m] = new float*[M - 1];
    for (int n = 0; n<M - 1; n+=1) {
      a[m][n] = new float[2];
    }
  }
}

我的计算不正确，我分配的空间接近 38GB.我现在修复了代码以分配 15GB.

#include <iostream>

using namespace std;
int main(int argc, char* argv[]) {
  unsigned long  N = 22000;
  unsigned long  M = 44100;
  unsigned long blk_dim = N*(M-1)*2;
  float* blk = new float[blk_dim];
  unsigned long b = (unsigned long) blk;

  float*** a = new float**[N];
  for (int m = 0; m<N; m+=1) {
    unsigned long offset1 = m*(M - 1)*2*sizeof(float);
    a[m] = new float*[M - 1];
    for (int n = 0; n<M - 1; n+=1) {
      unsigned long offset2 = n*2*sizeof(float);
      a[m][n] = (float*)(offset1 + offset2 + b);
    }
  }
}

float*** a = new float**[N];

a[m] = new float*[M - 1];

a[m][n] = new float[2];